I found a mode matching solution to match the beam coming to the PSL table from the AP table so that I can lock the laser beam coming onto the PSL table to the reference cavity on the table. I determined that at the polarizing beam splitter, I want a beam with a q=(147+25.1i)mm (w0=58mm). This came from applying the ABCD matrices for three distances,

• d1=693 mm,
• d12=660.4 mm, and
• d2=393.7 mm, separated
• an f=229.1 mm planoconvex lens and
• an R=300 mm curved mirror.

to a beam with q0 = 406.4i mm (w0=0.371 mm at the PMC).

I obtained the following mode matching solution, which I will try to implement on the PSL table:

The beam I have has waist 0.281 mm at -2.74 m (I set my origin at the polarizing beam splitter--the spot where I want my beam to match the beam coming from the PMC, so all waists are behind that point). These numbers  come from the beam-profiling and MATLAB-fitting I did (see 5015).

The solution I chose was: f = 1145.6 mm at -0.95 m and f = 572.7 mm at -0.62 m. This may need to be changed however, if I need to add in some beam steering, which would increase the path length traveled by the beam.